Forward kinematics

Summary

In robot kinematics, forward kinematics refers to the use of the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters. The kinematics equations of the robot are used in robotics, computer games, and animation. The reverse process, that computes the joint parameters that achieve a specified position of the end-effector, is known as inverse kinematics. Kinematics equations The kinematics equations for the series chain of a robot are obtained using a rigid transformation [Z] to characterize the relative movement allowed at each joint and separate rigid transformation [X] to define the dimensions of each link. The result is a sequence of rigid transformations alternating joint and link transformations from the base of the chain to its end link, which is equated to the specified position for the end link, :[T] = [Z_1][X_1][Z_2][X_2]\ldots[X_{n-1}][Z_n],! where [T] is the transformation locat

Official source

https://en.wikipedia.org/wiki/Forward_kinematics

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Orion MinAngle: A flexure-based, double-tilting parallel kinematics for ultra-high precision applications requiring high angles of rotation

Reymond Clavel, Patric Pham

If you need to design ultra-high precision devices for mechanisms with multiple axes there are not a lot of ways leading around flexure-based joints. Using this type of articulations totally eliminates backlash and friction and is, by this, providing an accurate mechanical foundation for your device. The most important disadvantage of this technology is the low range of motion. The basic joint types, blades and circular hinges, have angular limits which strongly depend on the targeted stiffness, the quantity of motion cycles and the elastic limit of the material. This article will introduce novel parallel kinematics which are totally based on 1 dof flexures and whose angular range of motion is determined by twice the range of the single joint. It is a 3 dof parallel kinematic based on 3 identical kinematic chains which produce movements in θx, θy and z. The model has been designed to constitute the left hand of a machine tool that requires orienting the workpiece in a very precise manner and with high rotation amplitudes. Additionally to this it presents very interesting characteristics of Remote-Center-of-Motion (RCM) mechanisms. This is a vital feature for applications where the linear movements are highly limited and should not be consumed by parasitic movements of other axes. All these features, combined with the advantages of parallel kinematics, make the Orion MinAngle a very interesting concept. The model has been designed with joints achieving ±7.6° leading to an output angle of ±15° on both rotation axes. The study has shown really promising results concerning the mechanical properties, the high rotation angles and the RCM capabilities. The paper presents the kinematics and its optimization method which is used to guarantee a nearly perfect division of the output angle on all pivots of the mechanism. The next chapters talk about the dimensioning of the flexible joints and generally about the design of the robot. The last part of the paper verifies the optimization trough kinematic modeling of the robot and computes the mechanical properties like stiffness, internal strains and mechanical Eigenfrequencies. At the end we propose a realistic application as a 5-axes parallel-kinematic machine tool and we come to a conclusion about the potential of the Orion MinAngle mechanism.

2005

The Hita-STT is a five-axis parallel kinematics machine-tool designed for machining and polishing complex parts for applications in medical, automotive components, watch industries. The kinematics of Hita-STT prototype presents an over-constrained design in order to have constant stiffness in the entire workspace. This over-constraining is one of the causes of the hysteresis measured on the machine. Solutions to avoid hysteresis without degrading rigidity are presented. The machine has to be calibrated before its industrialization. A repeatability of 5 microns and an accuracy of 10 microns have to be reached in the entire workspace. Several calibration methods are presented and compared for the case of the Hita-STT machine-tool.

2006

A new 3 degrees of freedom (dof) structure is presented. It features rotation on two axes with a fixed remote center of motion (RCM) i.e. it always aims at the same point. The third axis is a linear movement in direction of the fixed point. This type of kinematics is useful for many applications where a parasitic translational movement during the rotation is undesirable. The kinematics is based on the well known Delta robot. It is in fact composed of two Deltas mounted on the same command arms, which are linked to the rotary actuators. Therefore the two Delta robots move in the same manner except that the one fixed at the end of the bars moves of a bigger amount than one fixed closer to the actuators. The two nacelles are then connected through a sliding universal joint and a ball-and-socket joint to the output. This connection represents the output of the robot. To guarantee a perfect RCM there needs to be a certain ratio between some geometric parameters of the machine. This ratio is based on the Thales theorem and will be explained in details in this article. The paper will also present the detailed kinematics and its optimization, some construction details of the prototype and geometric model. At the end we will propose some applications as well as the needed modifications to guarantee application specific performance.

2006

Orion MinAngle: A flexure-based, double-tilting parallel kinematics for ultra-high precision applications requiring high angles of rotation

Reymond Clavel, Patric Pham

2005